Simplify the following expression: $ k = 1 + \dfrac{7a}{-4a + 2} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-4a + 2}{-4a + 2}$ $ \dfrac{1}{1} \times \dfrac{-4a + 2}{-4a + 2} = \dfrac{-4a + 2}{-4a + 2} $ Therefore $ k = \dfrac{-4a + 2}{-4a + 2} + \dfrac{7a}{-4a + 2} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-4a + 2 + 7a}{-4a + 2} $ $k = \dfrac{3a + 2}{-4a + 2}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{-3a - 2}{4a - 2}$